arXiv Machine Learning

Error Analysis of Neural-Network-Based Engression

arXiv:2607. 27723v1 Announce Type: cross Abstract: Engression (Shen and Meinshausen, 2024) learns a conditional distribution by fitting a generative model $Y = f(X,\varepsilon)$ under the energy score, a strictly proper scoring rule.

arXiv Machine Learning
Sep 25

Sufficiently Reduced Distributional Regression

Sufficiently Reduced Distributional Regression (SRDR) is a generative approach that merges conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). By framing SDR as a risk minimization problem using strictly proper scoring rules, SRDR jointly learns a dimension reduction map and a generative prediction model through minimization of the energy score, which can be estimated via sampling. The method extends to multi‑environment data and classification, and theoretical results show convergence of estimated conditional distributions in energy distance, implying asymptotic sufficiency. In experiments on CT slice localization, superconductivity data, and digit classification, SRDR recovers low‑dimensional sufficient structure and matches or surpasses state‑of‑the‑art nonlinear SDR methods in representation quality and predictive performance.

By Alexander Henzi, Tiange Liu, Xinwei Shen
arXiv AI
Jun 24

Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate

arXiv:2606. 23920v1 Announce Type: cross Abstract: The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions.

By Duncan Soiffer, Chandler Squires, Yuan Guan, Jason Hartford, Pradeep Ravikumar
arXiv AI
Aug 25

Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks

The paper presents a theoretical framework for approximating ratio-type functionals that arise in conditional generative modeling, specifically when the target density is expressed as a ratio of two kernel-based marginal densities. It proves that deep neural networks using the SignReLU activation can approximate these ratios with established L^p(Omega) bounds and convergence rates under standard regularity assumptions. Applying the framework to Denoising Diffusion Probabilistic Models, the authors construct a SignReLU-based estimator for the reverse process and derive bounds on the excess Kullback–Leibler risk, decomposing it into approximation and estimation errors to provide generalization guarantees for finite-sample training.

By Luwei Sun, Dongrui Shen, Feng Chuanwen, Jianfe Li, Yulong Zhao, Han Feng
arXiv AI
3d ago

BayesNDE: Bayesian Generative Modeling for Neural Density Estimation

BayesNDE is a neural density estimator that uses Bayesian generative modeling to estimate densities without relying on invertible networks or Jacobian-determinant calculations. It constructs an adaptive proposal for each observation by inferring a sample-specific latent posterior, and then applies bridge sampling to combine proposal samples with separate posterior samples for density estimation. Experiments on synthetic datasets show improved density estimation and structure recovery, while real-world applications demonstrate better anomaly detection.

By Chenglin Li, Qiao Liu